The passage to the continuous in the theory developed
in [1]} consists in the construction of a suitable \(C^*\) -algebra \({C}_B\)  of magnetic operators acting on \(L^2\big (\mathbb {R}^2\big )\) 
and an associated spectral triple which provides the right index theory for the
topological interpretation of the QHE. The construction of the magnetic
algebra \({C}_B\)  (still called noncommutative Brillouin zone
in [1]}) is standard in the literature and is
related to the abstract theory of group \(C^*\) -algebras (see Section REF  for more details). However, \({C}_B\)  can also be introduced
in a very concrete way. Let \(\lbrace \psi _{n,m}\rbrace \subset L^2\big (\mathbb {R}^2\big )\) , with
\(n,m\in \mathbb {N}_0:=\mathbb {N}\cup \lbrace 0\rbrace \)  be the orthonormal basis provided be the
generalized Laguerre functions (REF ), and define the family of operators
\(\Upsilon _{j\mapsto k}\psi _{n,m} := \delta _{j,n} \psi _{k,m} ,\qquad k,j,n,m\in \mathbb {N}_0 .\) 
